It looks like we the series is
[tex]\displaystyle\sum_{n=1}^\infty\frac{8\cdot16\cdot24\cdot\cdots\cdot(8n)}{n!}[/tex]
In the numerator, we can factor out [tex]n[/tex] copies of 8:
[tex]\displaystyle\sum_{n=1}^\infty\frac{8^n(1\cdot2\cdot3\cdot\cdots\cdot n}{n!}=\sum_{n=1}^\infty\frac{8^nn!}{n!}=\sum_{n=1}^\infty8^n[/tex]
Then [tex]a_n=8^n[/tex] and by the ratio test,
[tex]\displaystyle\lim_{n\to\infty}\left|\dfrac{8^{n+1}}{8^n}\right|=\lim_{n\to\infty}8=8>1[/tex]
so the series diverges.
